Here, too, on this question of the ‘true end of knowledge’ a temperamental difference parts the new rationalists and empiricists. A Galileo or Descartes would not have been as inclined to archly dismiss ‘pleasure of the mind’ or ‘lust of knowledge’ as Bacon had been. Though the scientific rationalists and scientific empiricists might share the belief that experience must be subjected to special treatment to be rendered profitable for science, they had differing views on the profit of science. The experimental/empiricists (Gilbert, Harvey) tended to agree with Bacon’s practical goals. As men must experimentally assert their power over nature, so, too, the value of possessing nature’s secrets was that they be utilised for the practical improvement of men’s lives. For the mathematical/rationalists the knowledge was sufficient unto itself, a thing deserving to be desired, whether it yielded practical improvements or not.
By 1660, the mathematical understanding of physical explanation could not be ignored, not with the work of people like Copernicus, Galileo and Descartes; and the men who came together to form a Colledge for the Promoting of Physico-Mathematicall Experimentall Learning acknowledged the mathematical conception of the physical in their self-designation. Nevertheless by temperament these early men of the Royal Society were more allied with Bacon, Gilbert and Harvey than with Galileo and Descartes. It was the ‘experimentall learning’ that most engaged them, and so, too, they were inclined to embrace the practical humanitarian goals of science that Bacon had linked with his experimentalism.
Christopher Wren gave the inaugural lecture at Gresham College, after the Royal Society had been officially formed in 1662, and in his address he spoke passionately of the manner in which the new thinking had thrown off the tyranny of the old system of thought, bringing in its stead the freedom of scientific investigation. In the course of his celebratory advocacy he extolled William Gilbert (chastised by Galileo for his lack of geometry) as the very embodiment of the new science:
Among the honourable Assertors of this Liberty, I must reckon Gilbert, who having found an admirable Correspondence between his Terrela, and the great Magnet of the Earth, thought, this Way, to determine this great Question, and spent his studies and Estate upon this Enquiry; by which obiter, he found out many admirable magnetical Experiments: This Man would I have adored, not only as the sole Inventor of Magneticks, a new Science to be added to the Bulk of Learning, but as the Father of the new Philosophy.
But if any thinker hovered as a guiding spirit over the group it was the thoroughly empiricist Francis Bacon. Bacon had dreamed of a science that would operate in the way of a collaboration, a ‘Fellowship’ to take the place of individual geniuses working in isolation; it was all of a piece with his utopian ambitions for the new knowledge, and the members of the Royal Society called themselves ‘Fellows’ in homage to the Lord Chancellor’s vision.
And yet intimations of a union between the ‘physico-mathematicall’ and ‘experimentall’ there had no doubt been. It is in the chemist Robert Boyle, the most important scientist among the twelve original Fellows, that we can see the two approaches groping somewhat dazedly toward one another. Boyle was certainly, in many ways, a disciple of Bacon – but not in all ways. He preserved an interest in the practical control of nature through knowledge of cases, which had been such a prominent feature in Francis Bacon, and which both men regarded as closely related to the empirical method; and yet he also had been touched by the Galilean spirit. Though not himself a profound mathematician, Boyle was keenly aware that astronomy and mechanics had outstripped chemistry. He was eager to carry chemistry forward by allying it with an atomistic interpretation of matter, and he recognised that mathematics was integral to the atomistic interpretation of physical phenomena.
But he also contended that chemistry, in its vigorous experimentalism, had something to teach the fields of astronomy and mechanics that had been so transformed by its mathematical reconfiguration. These latter endeavours ‘have hitherto presented us rather a mathematical hypothesis of the universe than a physical, having been careful to show us the magnitudes, situations, and motions of the great globes, without being solicitous to declare what simpler bodies, and what compounded ones, the terrestrial globe we inhabit does or may consist in’.10
Boyle’s suggestion is that the new science, as understood by Galileo et al., is all very well and good, but that, in its overly abstract mathematical demonstrations and idealised formulations, it had travelled too far in the direction of apriorism. Robert Boyle is proposing that chemistry, though lagging behind on the theoretical side, might yet have something to offer the fledgling methodology in the way of getting one’s hands stained with the stuff of ‘the terrestrial globe we inhabit’. His distinction between mathematical and physical hypotheses is important, and we shall see it again. It reveals Boyle’s intuition that there was still something missing in the systems of Galileo and Descartes, no matter how impressive they were.
It is relevant that Boyle was a chemist. The example of the alchemists, though they strayed too near to mysticism and magic for Boyle’s taste, was not purely negative, for they had defied the old system’s passivity toward nature. (Bacon, too, had praised alchemy as a scientia operativa.)
But though Boyle seemed to have sensed the presence of a unified methodology binding together the activist approaches of the new rationalism and new empiricism, he does not manage to bring it forth, perhaps because he himself lacked mathematical muscle. 11 The best that he can offer is a reconciliation wrought by relativism: if what one is after is knowledge of nature then quantitative deductions on the model of Galileo and Cartesianism will yield satisfaction; but if one’s aim is control of nature in
An undated example of Robert Boyle’s writing on chemistry – ‘Effects of the varying Weights of the Atmosphere upon some bodies in the Water…’
the interest of particular ends, the necessary relations can often be discovered between qualities immediately experienced or drawn forth from experiments. It all depends on what one wants out of one’s science, he writes, although the implication is that true knowledge, if that’s what one wants, will require something more deductive than experimental.
The true blending of the two rivals for replacing the teleological understanding of explanation finally arrived in a work whose very title is telling: Philosophiæ Naturalis Principia Mathematica , The Mathematical Principles of Natural Philosophy. With Isaac Newton, a scientist who saw mathematics as essential to physical understanding had entered the ranks of the Royal Society. And yet the experimental aspect is also of fundamental importance to his methodology.
The title page of Principia. The inscription is written by John Flamsteed noting that the book is a gift from the author – Newton.
Newton observes in his preface to the Principia that ‘all the difficulty of philosophy seems to consist in this – from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena’. The phrase to ‘demonstrate the other phenomena’ reiterates the message of the work’s title: the fundamental place of mathematics in Newton’s method:
We offer this work as mathematical principles of philosophy. By the propositions mathematically demonstrated in the first book, we then derive from the celestial phenomena the forces of gravity with which bodies tend to the sun and the several planets. Then, from these forces, by other propositions which are also mathematical, we deduce the motions of the planets, the comets, the moon, and the sea.
As it was for Aristotle, so it was for Newton: to investigate nature is to investigate motions. Only, of course, Newton has inherited Galileo’s transformed conception of motion, reconfigured by, and restricted to, mathematical expression. The mathematical imagination of Newton, surpassing that of Galileo or Descartes, made possible the mathematical absorption of far vaster reaches